Towards Correctness of Program Transformations Through Unification and Critical Pair Computation

Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules, and then of so-called complete sets of diagrams. The method is similar to the computation of critical pairs for the completion of term rewriting systems. We explore cases where the computation of these overlaps can be done in a first order way by variants of critical pair computation that use unification algorithms. As a case study we apply the method to a lambda calculus with recursive let-expressions and describe an effective unification algorithm to determine all overlaps of a set of transformations with all reduction rules. The unification algorithm employs many-sorted terms, the equational theory of left-commutativity modelling multi-sets, context variables of different kinds and a mechanism for compactly representing binding chains in recursive let-expressions.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Graviweak Unification

The coupling of chiral fermions to gravity makes use only of the selfdual SU(2) subalgebra of the (complexified) SO(3,1) algebra. It is possible to identify the antiselfdual subalgebra with the SU(2)_L isospin group that appears in the Standard Model, or with its right-handed counterpart SU(2)_R that appears in some extensions. Based on this observation, we describe a form of unification of the gravitational and weak interactions. We also discuss models with fermions of both chiralities, the inclusion strong interactions, and the way in which these unified models of gravitational and gauge interactions avoid conflict with the Coleman-Mandula theorem.Comment: 18 pages, typos corrected and improved wordin

Simulation Subsumption or Déjà vu on the Web

Simulation unification is a special kind of unification adapted to retrieving semi-structured data on the Web. This article introduces simulation subsumption, or containment, that is, query subsumption under simulation unification. Simulation subsumption is crucial in general for query optimization, in particular for optimizing pattern-based search engines, and for the termination of recursive rule-based web languages such as the XML and RDF query language Xcerpt. This paper first motivates and formalizes simulation subsumption. Then, it establishes decidability of simulation subsumption for advanced query patterns featuring descendant constructs, regular expressions, negative subterms (or subterm exclusions), and multiple variable occurrences. Finally, we show that subsumption between two query terms can be decided in O(n!n) where n is the sum of the sizes of both query terms

Four Lessons in Versatility or How Query Languages Adapt to the Web

Exposing not only human-centered information, but machine-processable data on the Web is one of the commonalities of recent Web trends. It has enabled a new kind of applications and businesses where the data is used in ways not foreseen by the data providers. Yet this exposition has fractured the Web into islands of data, each in different Web formats: Some providers choose XML, others RDF, again others JSON or OWL, for their data, even in similar domains. This fracturing stifles innovation as application builders have to cope not only with one Web stack (e.g., XML technology) but with several ones, each of considerable complexity. With Xcerpt we have developed a rule- and pattern based query language that aims to give shield application builders from much of this complexity: In a single query language XML and RDF data can be accessed, processed, combined, and re-published. Though the need for combined access to XML and RDF data has been recognized in previous work (including the W3C’s GRDDL), our approach differs in four main aspects: (1) We provide a single language (rather than two separate or embedded languages), thus minimizing the conceptual overhead of dealing with disparate data formats. (2) Both the declarative (logic-based) and the operational semantics are unified in that they apply for querying XML and RDF in the same way. (3) We show that the resulting query language can be implemented reusing traditional database technology, if desirable. Nevertheless, we also give a unified evaluation approach based on interval labelings of graphs that is at least as fast as existing approaches for tree-shaped XML data, yet provides linear time and space querying also for many RDF graphs. We believe that Web query languages are the right tool for declarative data access in Web applications and that Xcerpt is a significant step towards a more convenient, yet highly efficient data access in a “Web of Data”

XRound : A reversible template language and its application in model-based security analysis

Successful analysis of the models used in Model-Driven Development requires the ability to synthesise the results of analysis and automatically integrate these results with the models themselves. This paper presents a reversible template language called XRound which supports round-trip transformations between models and the logic used to encode system properties. A template processor that supports the language is described, and the use of the template language is illustrated by its application in an analysis workbench, designed to support analysis of security properties of UML and MOF-based models. As a result of using reversible templates, it is possible to seamlessly and automatically integrate the results of a security analysis with a model. (C) 2008 Elsevier B.V. All rights reserved

Gauge Unification in Higher Dimensions

A complete 5-dimensional SU(5) unified theory is constructed which, on compactification on the orbifold with two different Z_2's (Z_2 and Z_2'), yields the minimal supersymmetric standard model. The orbifold accomplishes SU(5) gauge symmetry breaking, doublet-triplet splitting, and a vanishing of proton decay from operators of dimension 5. Until 4d supersymmetry is broken, all proton decay from dimension 4 and dimension 5 operators is forced to vanish by an exact U(1)_R symmetry. Quarks and leptons and their Yukawa interactions are located at the Z_2 orbifold fixed points, where SU(5) is unbroken. A new mechanism for introducing SU(5) breaking into the quark and lepton masses is introduced, which originates from the SU(5) violation in the zero-mode structure of bulk multiplets. Even though SU(5) is absent at the Z_2' orbifold fixed point, the brane threshold corrections to gauge coupling unification are argued to be negligibly small, while the logarithmic corrections are small and in a direction which improves the agreement with the experimental measurements of the gauge couplings. Furthermore, the X gauge boson mass is lowered, so that proton decay to e^+ \pi^0 is expected with a rate within about one order of magnitude of the current limit. Supersymmetry breaking occurs on the Z_2' orbifold fixed point, and is felt directly by the gauge and Higgs sectors, while squarks and sleptons acquire mass via gaugino mediation, solving the supersymmetric flavor problem.Comment: 21 pages, Latex, references added, final versio